Optimal. Leaf size=12 \[ (-3+e) \left (-5-\frac {5}{x^2}+x\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.58, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14}
\begin {gather*} \frac {5 (3-e)}{x^2}-(3-e) x \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-3 \left (1-\frac {e}{3}\right )+\frac {10 (-3+e)}{x^3}\right ) \, dx\\ &=\frac {5 (3-e)}{x^2}-(3-e) x\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} (-3+e) \left (-\frac {5}{x^2}+x\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.05, size = 13, normalized size = 1.08
method | result | size |
default | \(\left ({\mathrm e}-3\right ) \left (x -\frac {5}{x^{2}}\right )\) | \(13\) |
gosper | \(\frac {\left ({\mathrm e}-3\right ) \left (x^{3}-5\right )}{x^{2}}\) | \(14\) |
norman | \(\frac {\left ({\mathrm e}-3\right ) x^{3}-5 \,{\mathrm e}+15}{x^{2}}\) | \(19\) |
risch | \(x \,{\mathrm e}-3 x -\frac {5 \,{\mathrm e}}{x^{2}}+\frac {15}{x^{2}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 16, normalized size = 1.33 \begin {gather*} x {\left (e - 3\right )} - \frac {5 \, {\left (e - 3\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 21, normalized size = 1.75 \begin {gather*} -\frac {3 \, x^{3} - {\left (x^{3} - 5\right )} e - 15}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 17, normalized size = 1.42 \begin {gather*} - x \left (3 - e\right ) - \frac {-15 + 5 e}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 17, normalized size = 1.42 \begin {gather*} x e - 3 \, x - \frac {5 \, {\left (e - 3\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 13, normalized size = 1.08 \begin {gather*} \frac {\left (x^3-5\right )\,\left (\mathrm {e}-3\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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